Prepare the Dough: In the bowl of your stand mixer fitted with the dough hook, begin by mixing the flour, sugar, and instant yeast. Next, pour in the lukewarm milk and the eggs (preferably beaten together beforehand), then start kneading on medium speed for about 3 minutes, until a dough begins to form.

Add the Salt: Incorporate the salt and continue to knead for an additional two minutes. At this point, the dough will be a bit sticky, but it should start pulling away from the sides of the bowl.

Incorporate the Butter: Now it's time to add the soft butter, one small piece at a time. Wait for each piece to be fully incorporated before adding the next. Once all the butter is mixed in, increase the speed and knead for about 15 minutes. The dough should become smooth, very elastic, and shiny. To check if it's ready, perform the "windowpane test": gently stretch a small piece of dough between your fingers. If you can form a nearly transparent membrane without it tearing, the gluten is sufficiently developed.

First Rise: Shape your dough into a ball, place it in a large bowl, and cover it with a clean kitchen towel. Let it rise in a warm place for about 1.5 hours, or until it has visibly doubled in size.

Divide the Dough: Once the dough has risen, gently punch it down to deflate it. Transfer it to a lightly floured work surface. For perfectly equal portions, weigh the dough and divide the total weight by 8, then cut your 8 pieces.

Shape the Rolls: Take one piece of dough and gently flatten it with your fingers. Sprinkle some of the chocolate chips over the surface. Fold the edges toward the center to enclose the chocolate and form a ball. Flip the ball over (seam-side down) and drag it on the counter towards you to create a slight surface tension, which ensures a nice, round shape. Repeat this process for the other 7 pieces of dough.

Second Rise: Prepare your loaf pan (approx. 11.5x30 cm / 4.5x12 inches) by greasing and flouring it. Arrange the 8 brioche rolls inside in a zigzag pattern for a beautiful result. Generously brush the tops with the beaten egg for the egg wash, and if you're feeling indulgent, add a few more chocolate chips. Cover again with the kitchen towel and let it rise one last time for 30 to 45 minutes.

Baking: During the second rise, preheat your oven to 180°C (350°F). Bake the brioche for 20 to 30 minutes, until it is well-risen and has a beautiful golden-brown color. Let it cool completely in its pan before removing it to enjoy.